The basic techniques for electromagnetic logging for earth formations are well known. For instance, induction logging to determine resistivity (or its inverse, conductivity) of earth formations adjacent a borehole has long been a standard and important technique in the search for and recovery of hydrocarbons. Generally, a transmitter transmits an electromagnetic signal that passes through formation materials around the borehole and induces a signal in one or more receivers. The properties of the signal received, such as its amplitude and/or phase, are influenced by the formation resistivity, enabling resistivity measurements to be made. The measured signal characteristics and/or formation properties calculated therefrom may be recorded as a function of the tool's depth or position in the borehole, yielding a formation log that can be used to analyze the formation.
The resistivity of a given formation may be isotropic (equal in all directions) or anisotropic (unequal in different directions). In electrically anisotropic formations, the anisotropy is generally attributable to extremely fine layering during the sedimentary build-up of the formation. As a result, in a formation Cartesian coordinate system oriented such that the x-y plane is parallel to the formation layers and the z axis is perpendicular to the formation layers, resistivities Rx and Ry in the x and y directions, respectively, tend to be similar, but resistivity Rz in the z direction tends to be different. The resistivity in a direction parallel to the formation plane (i.e., the x-y plane) is known as the horizontal resistivity, Rh, and the resistivity in the direction perpendicular to the plane of the formation (i.e., the z direction) is known as the vertical resistivity, Rv. The index of anisotropy, η, is defined as η=[Rv/Rh]1/2.
As a further complication to measuring formation resistivity, boreholes are generally perpendicular to formation beds. The angle between the axis of the well bore and the orientation of the formation beds (as represented by the normal vector) has two components. These components are the dip angle and the strike angle. The dip angle is the angle between the borehole axis and the normal vector for the formation bed. The strike angle is the direction in which the borehole's axis “leans away from” the normal vector.
Electromagnetic resistivity logging measurements are a complex function of formation resistivity, formation anisotropy, and the formation dip and strike angles, which may all be unknown. Logging tools that fail to account for one or more of these parameters may produce inaccurate measurements. Moreover, tools that are able to provide dip and strike measurements along with azimuthal orientation information can be used to adjust the drilling direction to increase the borehole's exposure to a hydrocarbon bearing formation (“geosteering”). Specifically, it is desirable to be able to steer a tool to an underground target using the information available from the logging tool. Moreover, it is desirable to be able to match raw measurements to the modeled response for the system to evaluate the system performance.